Rat Race appears to have been based on the STL "Sprite" ROM and "Tune" ROM (I don't see it on disks STL1-10, but I have a copy). Other than that, it's just a BASIC program copied into SWR.

How does a BASIC program run from SWR given that the BASIC interpreter would be occupying the same address space?

I haven't checked this specific ROM, but the standard pattern is that on startup the program is copied down into RAM, then BASIC invoked with something like "PAGE=&1900|MOLD|MRUN|M" in the keyboard buffer.